Stochastic gradient method with accelerated stochastic dynamics

International Meeting on High-Dimensional Data-Driven Science 2015

Ohzeki, Masayuki^1

Department of Systems Science, Graduate School of Informatics, Kyoto University, 36-1 Yoshida Hon-machi, Sakyo-ku, Kyoto

606-8501, Japan^1

关键词: Computational costs;    Convergence speed;    Correlation time;    Detailed balance;    Stationary state;    Stochastic dynamics;    Stochastic gradient;    Stochastic gradient methods;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/699/1/012019/pdf
DOI  :  10.1088/1742-6596/699/1/012019

来源: IOP

【 摘 要 】

We implement the simple method to accelerate the convergence speed to the steady state and enhance the mixing rate to the stochastic gradient Langevin method. The ordinary stochastic gradient method is based on mini-batch learning for reducing the computational cost when the amount of data is extraordinary large. The stochasticity of the gradient can be mitigated by the injection of Gaussian noise, which yields the stochastic Langevin gradient method; this method can be used for Bayesian posterior sampling. However, the performance of the stochastic Langevin gradient method depends on the mixing rate of the stochastic dynamics. In this study, we propose violating the detailed balance condition to enhance the mixing rate. Recent studies have revealed that violating the detailed balance condition accelerates the convergence to a stationary state and reduces the correlation time between the samplings. We implement this violation of the detailed balance condition in the stochastic gradient Langevin method and test our method for a simple model to demonstrate its performance.